Skip to main content

Soliton Turbulence in Nonlinear Optical Phenomena

  • Chapter

Part of the book series: Progress in Nonlinear Differential Equations and Their Applications ((PNLDE,volume 11))

Abstract

Nonlinear optical physics, the study of the interaction of matter and intense electromagnetic fields in the visible spectrum, has become a very exciting and fruitful research topic for the applied scientist. This area, which started some 30 years ago, has already produced important applications in laser technology, optical communications and data storage to name some, and has potential applications such as all optical logic devices. It is also a continuous source of current theoretical research in the area of integrable and near integrable equations. It is well known, for example, that the nonlinear Schrödinger (NLS) equation and variations thereof, governs the dynamics of pulses in nonlinear dielectrics. The robustness of the known soliton solutions of the NLS equation [1], has been verified experimentally as optical pulses have been shown to propagate undistorted for thousands of kilometers in optical fibers [2].

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. V.E. Zakharov and A.B. Shabat, Zh. Eksp. Teor. Fiz. 61, 118 (1971) (Soviet Physics JETP 34, 62 (1972)).

    Google Scholar 

  2. L.F. Mollenauer J.P. Gordon and M.N. Islam, IEEE J. of Quantum Electron. 22, 157 (1986); L.F. Mollenauer and K. Smith, Opt. Lett. 13, 675 (1988).

    Article  Google Scholar 

  3. K. Ikeda, H. Daido and O. Akimoto, Phys. Rev. Lett. 45, 709 (1980).

    Article  Google Scholar 

  4. D.W. McLaughlin, J.V. Moloney and A.C. Newell, Phys. Rev. Lett. 54, 681 (1985).

    Article  Google Scholar 

  5. S.A. Akhmanov, M.A. Vorontzov and V. Yu. Ivanov, Pis’ma Zh. Eksp. Teor. Fiz. 47, 611 (1988) (JETP lett. 47, 707 (1988)); S.A. Akhmanov, M.A. Vorontsov, V. Yu Ivanov, A.V. Larichev and N.I. Zheleznykh, J. Opt. Soc. Am. B 9, b78 (1992).

    Google Scholar 

  6. P.K. Jakobsen, S.G. Wenden, J.V. Moloney and A.C. Newell, “Turbulent patterns in wide-gain section lasers”, Annual Meeting Optical Society of America, Albuquerque NM. 1992.

    Google Scholar 

  7. E. Kuznetzov, A.C. Newell and V.E. Zakharov, Phys. Rev. Lett. 67, 3243 (1991); S. Dyachenko, A.C. Newell, A. Pushkarev and V.E. Zakharov, Physica D 57, 96 (1992).

    Article  Google Scholar 

  8. P. Coullet, L. Gl and F. Rocca, Opt. Commun. 70, 403 (1989).

    Article  Google Scholar 

  9. F.T. Arecchi, G. Giacomelli, P.L. Ramazza and S. Residori, Phys. Rv. Lett. 67, 3749 (1991).

    Article  Google Scholar 

  10. V.E. Zakharov, A.N. Pushkarev, V.F. Shvets and V.V. Yan’kov, Pis’ma Zh. Eksp. Teor. Fiz. 48, 79 (1988) (JETP Lett. 48, 83 (1988)); A.I. D’yachenko, V.E. Zakharov, A.N. Pushkarev, V.F. Shvets and V.V. Yan’kov, Zh. Eksp. Teor. Fiz. 96, 2026 (1989) (Sov. Phys. JETP 69, 1144 (1989)).

    Google Scholar 

  11. A.B. Aceves and S. Wabnitz, Phys. Lett. A 141, 37 (1989).

    Article  Google Scholar 

  12. A.B. Aceves, C. De Angelis and S. Wabnitz, “Generation of Solitons in a Nonlinear Periodic Medium”, Opt. Lett. 17, 1566 (1993).

    Article  Google Scholar 

  13. A.B. Aceves and S. Wabnitz, “On the solutions of waves propagating in periodic nonlinear structures”, preprint (1993).

    Google Scholar 

  14. E.A. Kuznetsov and A.V. Mikhailov, Teor. Mat. Fiz. 30, 303 (1977); D.J. Kaup and A.C. Newell, Lett. Nuovo Cimento 20, 325 (1977).

    Article  Google Scholar 

  15. A.V. Mikhailov, JETP Lett. 32, 174 (1980); D. David, J. Hamad and S. Shnider, Lett. in Math. Phys., 8, 27 (1984).

    Google Scholar 

  16. L. Brillouin, Wave propagation in periodic structures, McGraw-Hill, New York (1946).

    Google Scholar 

  17. C.M. de Sterke, Phys. Rev. A 45, 8252 (1992).

    Article  Google Scholar 

  18. D.N. Christodoulides and R.I. Joseph, Phys. Rev. Lett. 62, 1746 (1989).

    Article  Google Scholar 

  19. W. Chen and D.L. Mills, Phys. Rev. Lett. 58, 160 (1987); D.L. Mills and S.E. Trullinger, Phys. Rev. B 36, 6269 (1987).

    Article  Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1993 Springer Science+Business Media New York

About this chapter

Cite this chapter

Aceves, A.B. (1993). Soliton Turbulence in Nonlinear Optical Phenomena. In: Fitzmaurice, N., Gurarie, D., McCaughan, F., Woyczyński, W.A. (eds) Nonlinear Waves and Weak Turbulence. Progress in Nonlinear Differential Equations and Their Applications, vol 11. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0331-5_11

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-0331-5_11

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-6711-9

  • Online ISBN: 978-1-4612-0331-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics